Question: ${\sqrt[3]{648} = \text{?}}$
Solution: $\sqrt[3]{648}$ is the number that, when multiplied by itself three times, equals $648$ First break down $648$ into its prime factorization and look for factors that appear three times. So the prime factorization of $648$ is $2\times 2\times 2\times 3\times 3\times 3\times 3$ Notice that we can rearrange the factors like so: $648 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 = (2\times 2\times 2) \times (3\times 3\times 3) \times 3$ So $\sqrt[3]{648} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{3}$ $\sqrt[3]{648} = 2\times 3 \times \sqrt[3]{3}$ $\sqrt[3]{648} = 6 \sqrt[3]{3}$